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In this work, we introduce new construction methods for self-dual codes usinga Baumert-Hall array. We apply the constructions over the alphabets F_2 and F_4+ uF_4 and combine them with extension theorems and neighboring constructions.As a result, we construct 46 new extremal binary self-dual codes of length 68,26 new best known Type II codes of length 72 and 8 new extremal Type II codesof length 80 that lead to new 3-(80,16,665) designs. Among the new codes oflength 68 are the examples of codes with the rare \gamma= 5 parameter in W68;2.All these new codes are tabulated in the paper.

New Extremal binary self-dual codes from a Baumert-Hall array